Analysing the Sustainability of Fiscal Deficits in Developing Countries

Transcription

1 WP6.0: susain7.wpd Analysing he Susainabiliy of Fiscal Deficis in Developing Counries John T. Cuddingon* 30 July /31/97 revision Economics Deparmen Georgeown Universiy Washingon, D.C *wih he assisance of Shihua Lu, PhD candidae a Georgeown.

2 Analysing he Susainabiliy of Fiscal Deficis in Developing Counries by John T. Cuddingon This paper surveys he recen lieraure analysing fiscal defici susainabiliy, mos of which focuses on he U.S. and oher indusrial counries, in an aemp o assess is poenial usefulness in he developing counry conex. Boh he accouning approach and he presen value consrain (PVC) approach are considered. Typically, susainabiliy analyses for developing counries involve issues ha are no paricularly imporan in he indusrial counry conex. Reliance on seigniorage o finance deficis is ofen quaniaively much more imporan, alhough is use varies widely across LDCs. The disincion beween domesic and foreign-currency borrowing is cenral; concessional lending and grans may also make an imporan conribuion o fiscal finance. We consider generalizaions of he PVC approach o siuaions where money-financing of deficis is used and concessional financing is available. The simulaneous presence of domesic and foreign deb, which characerizes a growing number of LDCs, are also discussed. JEL Classificaion: F34 (Inernaional Lending and Deb Problems), E62 (Fiscal Policy) O23 (Fiscal and Moneary Policy in Developmen) O011 (Macroeconomic Analyses of Economic Developmen)

3 Analysing he Susainabiliy of Fiscal Deficis in Developing Counries "Susainabiliy" is perhaps he mos frequenly used buzzword in economic policy making circles in he 1990s: susainable developmen, susainable environmenal policies, susainable deb and defici levels. In he macroeconomic conex, policy makers and analyss are frequenly asked: Are curren levels of fiscal deficis or levels of public-secor 1 deb susainable? Are renewed capial inflows o LDCs in he early 1990s susainable?. These issues are imporan for developed and developing counries alike. This paper surveys he recen lieraure analysing fiscal defici (and, in some cases, curren accoun) susainabiliy, mos of which focuses on he U.S. and oher indusrial counries, in an aemp o assess is poenial usefulness in he LDC conex. Two concepual approaches have been used: he accouning approach he presen value consrain (PVC) approach. Alhough we briefly summarize he former, our emphasis is he PVC approach. The saring poin for boh is he (emporal) financing consrain of he governmen or consolidaed public secor, which is oulined in Secion 1. The accouning approach o susainabiliy or macro policy consisency is discussed in Secion 2. The presen value consrain or ineremporal budge consrain is derived in Secion 3; he appropriae inerpreaion of PVC es in he lieraure is hen discussed: Wha does i mean o es a budge consrain? We argue ha he PVC ess should no be inerpreed as ess of wheher a governmen is solven bu raher as ess of wheher is fiscal policy sance is susainable. Tha is, could he pas behaviour of key fiscal variables and he implied fiscal defici or surplus, as capured by simple ime series models in he economeric ess, be coninued indefiniely wihou encounering resisance by lenders? For his o be feasible, he fiscal policy mus no enail Ponzi scheme financing. From his perspecive, i is he behaviour (or willingness ) of he governmen s crediors ha ulimaely deermines he susainabiliy of a fiscal policy. The no Ponzi game (NPG) condiion employed in Secion 3 can, in some circumsances, be derived from or is equivalen o he ransversaliy condiion in he lender s uiliy maximizaion problem. This 1 / Of course, capial inflows o LDCs migh be desirable even if hey are unsusainable. Emphasizing his poin, Max Corden has quipped, The growh of a child is no susainable, bu desirable never he less! 1

4 is aken up in Secion 4, firs in a deerminisic seing and hen in a more general sochasic environmen. (This secion, which is somewha more echnical, can be omied on firs reading wihou lose of coninuiy.) Secion 5 (and he spreadshee examples in Appendix 2) provide some ransparen examples of susainable and unsusainable fiscal policy in he simple case where only domesic bond financing of fiscal deficis is possible. In realiy, of course, fiscal rules are likely o be more complicaed. Raher han rying o characerize hese rules, he economeric lieraure esing he PVC focuses on ime series properies of he primary surplus, deb, and in some cases, governmen spending and axaion, wihou explicily relaing hem via an economic model o (presumably) endogenous variables like he real ineres rae, GDP growh, inflaion, ec. Ideally, he uni roo and/or coinegraion-based ess of susainabiliy should employ long ime series (say annual observaions) on various macroeconomic variables. For mos LDCs, such long ime series are ypically no available, or are conaminaed by one or more regime shifs which invalidae he assumpion ha he daa are all from he same daa generaing process. We discuss he possibiliy of describing fiscal policy rules based on shorer ime series combined wih oher counry-specific informaion (such as he policy condiions or arges ariculaed in a counry s IMF and/or World Bank programs). The mehods in he lieraure can hen be used o sudy wheher he coninuaion of hese hypohesized rules ino he indefinie fuure is susainable or wheher his fiscal sance would ulimaely require levels of financing ha lenders would find objecionable. Secion 6 discusses various economeric mehods used o es susainabiliy of fiscal policy. The empirical findings for U.S. fiscal policy are reviewed. As he ess are based on differen auxiliary assumpions, hey someimes lead o differen conclusions. These are highlighed and he empirical validiy of he auxiliary assumpions is discussed. Secion 6 concludes wih Ahmed and Roger s (1995) exension of he PVC approach o he simulaneous susainabiliy of curren accoun deficis and fiscal deficis. Susainabiliy analyses for developing counries will in many cases involve issues ha are no paricularly imporan in he indusrial counry conex. Reliance on seigniorage o finance deficis is ofen quaniaively much more imporan, alhough is use varies widely across LDCs. The disincion beween domesic and foreign-currency borrowing is surely 2

5 cenral; concessional lending and grans may also make an imporan conribuion o fiscal finance. Secion 7 considers generalizaions of he PVC approach o siuaions where moneyfinancing of deficis is used and concessional financing is available. The simulaneous presence of domesic and foreign deb, which characerizes a growing number of LDCs, are also discussed. The lieraure ypically aggregaes he wo ypes of deb and considers a single NPG condiion or PVC. (See, e.g., Agenor and Moniel (1996, Chaper 4).) We argue ha correc reamen of his siuaion involves wo separae no Ponzi game condiions, one for domesic lenders and anoher for foreign lenders. Secion 8 concludes. 1. The Consolidaed Public-Secor Financing Consrain Analyses of fiscal policy susainabiliy as well as discussions abou he muual consisency of various macroeconomic objecives begin wih he financing consrain of he consolidaed public secor including he cenral bank. This consrain relaes he convenional defici, i.e. he primary defici plus nominal ineres paymens, o increases in inernal and exernal sources of financing, as follows: B S B M SURP i B 1 i B 1 (1) * where B, B, and M are domesic-currency deb insrumens ( bonds ), foreign-currency bonds, and he moneary base, respecively. The ilde (~) indicaes nominal variables; i * and i are nominal raes of reurn on domesic and foreign bonds. For analyical work, i is more convenien o rewrie (1) in real erms: B (s B ) M SURP % M 1 r B 1 (r )B 1 (2) where he absence of ildes on he financial socks and he defici indicaes real magniudes, 2 * i.e. nominal series deflaed by he domesic GDP deflaor. r and r are real raes of reurn 2 Discussions of defici susainabiliy focus on he relaionship beween real primary surpluses and he real value of deb. For mos counries, however, he bulk of deb is nonindexed nominal deb. In his conex, Woodford (1995) poins ou ha he deerminaion of he price level may depend on he oal quaniy of nominal liabiliies (moneary and nonmoneary) 3

6 on domesic and foreign bonds; s is he real exchange rae s =S P * /P (where P * is he foreign price level). is he real rae of depreciaion of he domesic currency. From (2), i is clear ha any aemp o deermine wha level of (real) primary fiscal defici (or surplus) is susainable mus involve assumpions abou reliance on seigniorage, as well as assumpions abou he relaive imporance of domesic and foreign sources of deb finance over ime. The presen value consrain approach o susainable fiscal policy was iniially developed o sudy indusrial counries. I was assumed ha seigniorage revenue was unimporan and all public secor deb was denominaed in domesic currency. Under hese assumpions he financing consrain simplifies o a simple dynamic equaion relaing he sock of deb carried forward from he previous period, inclusive of ineres, and he primary surplus o nex period s deb B : B (1r )B 1 SURP. (3) B is he ousanding deb a he end of period and r equals he ex pos reurn on governmen deb during period. As wih (1), equaion (3) may be inerpreed in nominal or real erms. On he oher hand, he auxiliary assumpions required in he economeric ess (discussed below in Secion 6) are more likely o be saisfied if we consider real deb (i.e. nominal deb divided by a same-currency price index such as he GDP deflaor or CPI). Hence, r and SURP are inerpreed as he real ineres rae and real primary surplus, respecively, in wha follows. Given ime pahs for r and SURP, he governmen financing consrain in (3) describes he ime pah of he sock of deb, i.e., he dynamics of deb accumulaion or decumulaion. Several hings are apparen from (3): & If he governmen runs a primary surplus equal o zero (SURP = 0), he sock of deb will grow a a rae equal o he ineres rae: B B B 1 r B 1. (4) & If he governmen runs a primary defici (SURP < 0), he sock of deb will grow a a raher han jus he nominal money supply. 4

7 & rae exceeding he ineres rae. 3 If he governmen runs a primary surplus (SURP > 0), he sock of deb will grow more slowly han he ineres rae. If he surplus more han offses ineres paymens on exising deb (i.e. he convenional surplus, SURP + r B -1, is posiive), hen he deb will acually shrink over ime. Boh he PVC ess of susainabiliy and he accouning approaches o he consisency of macro policy arges begin from (3), or more generally (1). 2. The Accouning Approach o Susainabiliy or Policy Consisency The so-called accouning approach is someimes viewed as an approach o fiscal susainabiliy. Oher auhors inerpre i as a way o assess he muual consisency among a number of macro policy arges. In any even, he approach focuses a paricular deb raio, ypically deb o GDP, b = B /Y. Rewriing (3), which is in levels, in erms of he deb/gdp raio yields: B Y (1r )B 1 (1g )Y 1 SURP Y (5) or: b 1r 1g b 1 surp (6) where g is he growh rae in GDP beween -1 and. Using (6), he change in he deb/gdp raio equals: b b b 1 r g 1g b 1 surp (7) & where surp = SURP /GDP. I follows immediaely ha: If he primary surplus/gdp raio is equal o zero, he deb/gdp raio will grow (or r. 3 / For a consan defici, however, he growh rae of he deb falls asympoically oward 5

8 shrink) a he rae r-g. & If he governmen runs a primary defici (surplus), he deb/gdp raio will grow a a rae exceeding (less han) r-g. In he accouning approach, a primary defici (or surplus) is defined as susainable if i generaes a consan (raher han ever-increasing) deb/gdp raio, given a specified GDP growh arge and consan real ineres rae. Thus, in he simple case where seigniorage revenue and foreign borrowing are ignored, he susainable primary surplus o GDP raio is deermined by seing he change in he deb/gdp raio in (7) equal o zero: surp r g 1g b. (8) This is he level of he primary surplus ha would be required each year o keep he deb/gdp raio consan a is curren level b. Applicaions of he accouning approach invariably consider he possibiliy of using seigniorage revenue as a source of fiscal finance. In his case, surp in (8) should be inerpreed as he primary surplus plus susainable seigniorage revenue (as a raio of GDP). The laer is calculaed by assuming ha he raio of real high-powered money o GDP is a negaive funcion of he inflaion rae. The arge inflaion rae is hen used o calculae he seady-sae moneary base/gdp raio and he resuling seigniorage. (See Anand and van Wijnbergen (1989) for a horough discussion of his approach and an ineresing applicaion o Turkey.) The accouning approach has also been used o assess he consisency among various 4 macroeconomic policy arges. Suppose he governmen has he following policy arges (denoed by *): (i) a consan deb/gdp raio b*, (ii) a arge GDP growh rae equal o g* and (iii) a primary surplus/gdp raio equal o surp*. Are hese policies arges muually consisen? In addressing his quesion, he accouning approach ypically assumes ha 4 Ofenimes he lieraure calls his an analysis of policy consisency. This is poenially misleading in i is referring o he consisency of policy arges, such as GDP growh or he arge deb raio, raher han he policy insrumens, which are direcly conrolled by he policy maker. 6

9 changes in he primary surplus will have no effec on eiher real ineres raes or GDP growh. This is surely unrealisic. Presumably, he equilibrium real ineres rae depends posiively on he level of governmen spending and/or he amoun borrowed. To answer he above quesion, one would ideally use a model ha endogenously deermines real ineres raes and he GDP growh rae. I would hen be possible o analyze how hese key macro variables are affeced by changes in fiscal policy variables. Alhough he accouning approach focuses on seady-sae deb raios, he corresponding dynamic equaion in (6) could be employed o ask various quesions abou ransiional dynamics. For example, wha ime pah of adjusmen in he primary surplus over x years will resul in a specified fall in he deb/gdp raio? Would a deb wrie off be helpful in achieving his deb raio arge? The primary shorcoming of he accouning approach is ha i aemps o deermine he financable fiscal defici by making assumpions ha liabiliies can coninue o grow a he growh rae of he economy s GDP, so ha deb/gdp raios remains consan. This leaves raher vague he role ha lenders ulimaely play in deermining wha deb sraegies are susainable and which are no. The PVC approach is more explici in his regard. 3. The Presen Value Consrain Approach The PVC approach begins wih he governmen financing consrain in level [i.e. (3) above] and ieraes i forward N periods o ge: B 1 M N j0 SURP j B N1. (1r) j1 (1r) N1 (9) In deriving (9) from (3), i has been assumed for exposiional simpliciy ha he (expeced) 7

10 real ineres rae is consan over ime. A generalizaion o ime varying ineres raes is considered below. Some of he economeric ess in Secion 5 require he (srong) assumpion ha he expeced real ineres rae is consan; ohers require only he assumpion ha he real ineres rae is saionary. 5 A his poin he co-called no Ponzi game (NPG) condiion is invoked o argue ha he las erm in (9) goes o zero in he limi: lim N B N1 0. (1r) N1 (10) This condiion saes ha he presen value of he governmen s deb in he indefinie fuure converges o zero. For his o happen, real deb B (in he numeraor) mus grow more slowly han he real ineres rae (which is he growh rae of he denominaor). The NPG condiion is ypically jusified by arguing ha lenders would presumably no be willing o allow he governmen o perpeually pay heir enire curren ineres obligaion merely by borrowing more. If lenders were willing o do his, (4) shows ha he deb would grow a a rae equal o he ineres rae. Hence he discouned deb in (10) would no converge o zero. Secion 4 below discussed he NPG condiion and is relaionship o he ransversaliy condiion in he lender s ineremporal uiliy maximizaion problem in greaer deail. Imposing he NPG condiion in (9) implies ha he governmen deb a any poin in ime mus equal he presen value of is expeced fuure primary surpluses: 5 Even his assumpion is no unconroversial. See Rose (1988). 8

11 B 1 M j0 SURP j (1r) j1. (11) Noe ha he real ineres rae mus be posiive for he presen value of fuure surpluses o be finie. David Wilcox (1989, pp ) elaboraes in he imporance of he PVC: Fiscal policy is consrained by he need o finance he defici. Virually any paern of deficis would be susainable if i were possible o borrow money, and pay he ineres by borrowing more. Indeed, in some model economies i is possible for he governmen o do exacly ha (Diamond 1965). In hose economies, which are labeled dynamically inefficien, an increase in curren deb has no implicaions for fuure surpluses. Governmens in dynamically efficien economies, on he oher hand, face a presen-value borrowing consrain, so-called because i saes ha he curren marke value of he deb equals he discouned sum of expeced fuure surpluses. Inerpreing Economeric Tess of he PVC or NPG Condiion The recen empirical lieraure, iniiaed by he seminal conribuion of Hamilon and Flavin (1986), ess he validiy of he PVC in (11) or equivalenly he NPG condiion (10). There is a quesion of how o inerpre such ess. Wha does i mean o es a budge consrain? Some auhors have inerpreed ess of (10 or (11) as solvency ess. For example, Agenor and Moniel (1996, 123) argue ha: The governmen is solven if he expeced presen value of he fuure resources available o i for deb service is a leas equal o he face value of is iniial [i.e. curren] deb sock. Under hese circumsances, he governmen will be able o service is deb on marke erms. Solvency hus requires ha he governmen s prospecive fiscal plans saisfy he presen-value budge consrain... On he oher hand, an opimizing governmen should never plan o have a sream of fuure primary surpluses wih a NPV sricly in excess of is curren deb, because his would imply lower governmen spending and/or higher axes han necessary o service he deb. Oher wriers inerpre he PVC ess as ess of he susainabiliy of curren fiscal 9

12 policy. Wilcox (1989, pp.293-4) conains an ineresing discussion on how o inerpre apparen violaions of he PVC: Hamilon and Flavin view heir ess as shedding ligh on wheher he governmen mus saisfy he borrowing consrain. If [he NPG condiion in (10) or he PVC in (11)] were violaed in he daa, Hamilon and Flavin would conclude ha he borrowing consrain need no be saisfied. By conras, I regard he necessiy of he presen-value borrowing consrain in a dynamically efficien economy as esablished on heoreical grounds...this suggess a naural definiion for he concep of susainabiliy: a susainable fiscal policy is one ha would be expeced o generae a sequence of deb and deficis such ha he presen-value borrowing consrain would hold...moreover, an unsusainable policy would be expeced o change... If he presen-value borrowing consrain does no hold, wha will be he form of he violaion? Hakkio and Rush (1991, p.429) also inerpre heir PVC ess as ess of he susainabiliy of curren fiscal policy: Is he [U.S.] budge defici oo large? Yes. Specifically, we find ha recen spending and ax policies of he governmen -- if coninued -- violae he governmen s ineremporal budge consrain. As a resul governmen sending mus be reduced and/or ax revenues mus be increased. The auhors sae explicily ha hey are esing wheher he NPG condiion would be saisfied if governmen revenue and expendiure coninued o follow heir pas sochasic processes. I conclude ha he PVC ess are appropriaely viewed as ess of he susainabiliy of he curren fiscal policy sance, as refleced in he hisorical imes series daa on governmen spending, revenue, deficis, and/or deb, no as solvency ess. An analysis of solvency would have o consider all conceivable governmen policies, and ask wheher here is any economically and poliically feasible policy sance ha would saisfy he PVC, given he value of curren deb. If here is none, hen he governmen is insolven. In he U.S. conex, i is reasonable o assume ha governmen expendiure or ax policies would ulimaely have o change in order o bring he projeced sream of discouned 10

13 fuure primary surpluses ino line wih he PVC in siuaions where he curren fiscal policy is unsusainable. In he LDC conex, on he oher hand, inflaionary surprises o wipe ou deb obligaions and/or deb repudiaion (or hreaening deb repudiaion in order o secure more favorable erms from crediors) may be enerained as policy opions. Presumably his arises when he poliical or economic coss of adjusing governmen expendiures or axes become oo high relaive o he coss of deb repudiaion. In shor, LDC governmens may become unwilling o pay before hey reach he poin where hey are unable o pay or insolven. Susainabiliy Tess Involving Deb Raios In order o relae he PVC ess o he accouning approach below, i is ineresing o recas NPG condiion in (10) or equivalenly he PVC in (11) in erms of raios. Ineresingly, an analysis based on raios is ofen moivaed by he argumen ha his is more appropriae for growing economies. For example, Hakkio and Rush (1991, p.430) noe: In addiion o examining real spending and revenue direcly, we also normalize hese variables by real GDP and populaion. This is an imporan exension beyond previous work since McCallum (1984), among ohers, deems hese raios -- per capia spending and revenue as a fracion of GNP -- as more perinen for a growing economy. I believe his saemen is false when applied o GDP growh, bu may be valid when populaion growh is involved. Consider he governmen financing consrain (3) in levels. One can always rewrie his consrain wih all variables expressed in erms of raios o any variable ha one migh care choose, be i GDP, populaion, or whaever (i.e. he world oupu of bananas). Defining b = B /Y as he relevan raio (e.g., using he deb o GDP raio in (5) above), he governmen financing consrain in (3) can be rewrien by dividing hrough by Y and using 11

14 he ideniy: Y 1 (1g ) Y. (12) where g is he growh rae in GDP beween -1 and. The resul looks like (5) above. Assuming for simpliciy ha r and g are consan over ime, recursive forward subsiuion in (3), using he definiion in (13), yields an expression analogous o (9), bu in raio form: b 0 M N j0 [ 1g 1r ](j1) SURP j Y j [ 1g 1r ](N1) B N1 Y N1. (13) The NPG condiion now appears o ake he form: lim N [ 1g 1r ](N1) B N1 Y N1 0. (14) Noe ha for he PVC or NPG condiions expressed in raio erms as in (13) or (14), respecively, he appropriae discoun facor (1+g)/(1+r) akes ino accoun he growh rae of he variable is used in he denominaor of he raio. Hakkio and Rush (1991, p.430) explain: When variables are nominal, he discoun facor is he nominal ineres rae; when variables are real, i is he real ineres rae; when variables are real per real GNP, i is he real ineres rae minus he rae of growh of real GNP; and when variables are real per capia, i is he real ineres rae minus he rae of populaion growh. A firs glance, he NPG condiion (14) seems o require ha r>g. In fac, his is no he case. The NPG condiion in (14) is idenical o ha in (10). Using he ideniy in (12), i is easy o see ha (14) does no depend on he growh rae in Y (regardless of wheher Y is real income or some oher variable). By similar reasoning, i can be shown ha he PVC wrien in erms of raios does no depend on g eiher: 12

15 b 1 M j0 (1r) (j1) SURP j (1g) (j1) Y j M j0 (1r) (j1) SURP j Y 0. (15) Given he above resul ha he conversion of he PVC and NPG condiions ino raio form leaves hem unaffeced, i is roublesome ha empirical analyses someimes arrive a differen conclusions using level and raio daa. (See especially Hakkio and Rush (1991).) A key issue when implemening he PVC ess is he saionariy of he variables being used. For coinegraion based ess, he variables in he coinegraing relaionship mus be I(1). I possible ha level series are I(1), bu he raio series are I(0). Thus, he decision o ransform he PVC ino raios may make he auxiliary assumpions associaed wih various ess (highlighed in Table 1 below) more or less plausible. When are he relaive magniudes of he real ineres rae and he growh rae of income relevan? Secion 5 provides an illusraion where he process deermining primary surplus SURP is assumed proporional o GDP. In his case, he presen value consrain can be rewrien in erms of raios o GDP and he difference beween he real ineres rae and he growh rae. Before leaving he discussion of he deb/gdp raio, i should be noed ha in some of he lieraure on fiscal defici susainabiliy, a differen definiion of susainabiliy is used. Fiscal policy is said o be susainable if he ime pah of he deb/gdp raio is bounded, i.e. 6 does no coninue o grow wihou limi. Is his crierion sronger han he PV consrain? Under circumsances where he real ineres rae is higher han he growh rae of GDP, he boundedness of deb o GDP is indeed a sronger crierion han he PV consrain. The PV consrain requires ha he growh rae of deb be less han he real ineres rae. This does no rule ou he possibiliy ha deb GDP raio increases wihou bound. If he real ineres rae is higher han GDP growh rae and he growh rae of deb is in beween hem, he PV 6 Hakkio and Rush (1991), for example, es boh he PV consrain and he boundedness of deb/gdp raio. 13

16 consrain is saisfied bu he deb GDP raio explodes over ime. On he oher hand, if deb GDP raio is bounded, he growh rae of deb has o be less han or a mos equal o he GDP growh rae. Given he real ineres rae is higher han he growh rae of GDP, PVC is cerainly saisfied. 14

17 4. Opimal Lender Behavior and he No Ponzi Game Condiion 7 The purpose of his secion is o discuss he siuaions where he NPG condiion can be derived from he lender s uiliy opimizaion problem. The deerminisic case wih zero populaion growh is a benchmark case. The cases of posiive populaion growh and a sochasic economy are hen considered in urn. McCallum (1984) considers a dynamical efficien economy in seady sae equilibrium. Assuming a consan ineres rae (as in (9) above), he shows ha he NPG condiion follows immediaely from he ransversaliy condiion of he lender s uiliy maximizaion problem. Tha is, he NPG condiion is an implicaion of opimal behavior by lenders. (See Appendix 1 for deails). Thus, Ponzi financing should no be possible if lenders are raional in deerminisic models wih consan populaion. Raional Ponzi Games O Connell and Zeldes (1988) discuss he possibiliy of raional Ponzi games. They explain how such schemes can arise when an economy s populaion is growing over ime and where here is no (or, a leas, no universal) inergeneraional alruism: New agens are born ino he economy and fend for hemselves. The key poin here is ha while each individual will saisfy his own ransversaliy condiion, his will no suffice o rule ou raional Ponzi games. Even hough each individual s wealh will no be growing faser han he inverse discoun facor, populaion growh may make i possible for aggregae desired wealh o grow a he rae of ineres or faser. Ponzi games are herefore feasible in an economy wih infinie-lived agens. (p.438) Ineresingly, hey noe ha: when borrowers are running raional Ponzi schemes, his does no imply ha lenders are in any sense losing ou. In he models we sudy in his paper, raional Ponzi games are only feasible when he economy is in a dynamically Pareo inefficien equilibrium. The inroducion of perpeually rolled over deb will never make he lending economy worse off and will in general make i beer off relaive o a world in which no Ponzi game is run. (p.433). Presumably, however, he lending economy could make iself even beer off by having is own governmen raher han foreigners run he Ponzi game!! In sum, he O Connell and Zeldes (1988) analysis concludes ha when he relevan populaion of lenders is growing, a modes Ponzi scheme is feasible. The ransversaliy 7 This secion may be omied on firs reading wihou loss of coninuiy. 15

18 condiion of individuals will imply ha, if he populaion is growing a rae n, say, he governmen deb mus grow a a rae less han r+n, no a rae less han r as presumed in he various susainabiliy ess. The ransversaliy condiion for an individual lender in economies wih growing populaions equals: lim N B N 0 (1r) N (1n) N (16) N where B is he aggregae sock of deb and hence B /(1+n) is deb per capia. The N governmen mus insure ha deb per capia grows a a rae less han he ineres rae in order o saisfy he ransversaliy condiions of all lenders in he economy. Thus, when he lender populaion is growing, susainabiliy ess should be based on he raios of deb and he primary surplus o he populaion. Taking raios o GDP, on he oher hand, is poenially confusing and in any even has no bearing on he PVC or NPG ess (as shown a he end of Secion 3), regardless of wheher GDP in eiher he debor or credior economy is growing. N Transversaliy Condiions in Uncerain Environmens Bohn (1995) noes ha he following wo empirical observaions can no be reconciled in a deerminisic seing: (i) he ineres raes on U.S. governmen bonds have been significanly below he average rae of he economic growh and (ii) according o he empirical analysis in Abel e al (1989), he U.S. economy is dynamic efficien. He goes on o argue ha hese wo hings can happen ogeher only in a sochasic environmen. Hence, i is more appropriae o examine he susainabiliy of fiscal policy by using ess ha are derived from sochasic models of he economy. The PVC in (11) and he NPG condiion in (10) were derived under he assumpion of consan real reurn on governmen deb. Here we relax ha assumpion by deriving he corresponding condiions for he case where he ex pos reurn on governmen deb r is sochasic and hence may vary from period o period. Wih non-consan r, forward ieraion of he governmen financing consrain in (3) and aking expecaions yields: B 1 E M j0 q j SURP j E q N B N (17) 16

19 where q j j i0 (1r i ) 1 (18) is he compound discoun facor relevan for period +j cashflows. The NPG condiion, herefore, equals: lim N E q N B N 0. (19) The resuling PVC is: B 1 E M j0 q j SURP j. (20) Wha is he general consrain on governmen borrowing in a sochasic seing? As Bohn (1995) shows, he lender s ineremporal budge consrain can be wrien as: (1r )B 1 M j0 E (s j SURP j ) lim N E [s N (1r N )B N 1 ]. (21) N where s +N = u (c +N)/u (c ) is he lender s marginal rae of ineremporal subsiuion beween periods and +N. (1+r )B is he lender s wealh (inclusive of ineres earned -1 beween -1 and ) going ino period. The ransversaliy condiion requires ha he lender s presen valuaion of fuure governmen liabiliies, he las erm on he righ-hand-side of (21), should go o zero in he limi: lim N E [s N (1r N )B N 1 ] 0. (22) The resuling PVC, herefore, equals: (1r )B 1 M j0 E [s j SURP j ]. (23) 17

20 Noice ha (22) and (23) are differen from (10) and (11) in ha hey use he marginal rae of ineremporal subsiuion insead of he real ineres rae as he discoun facor. The marginal rae of subsiuion is closely relaed o he risk-free ineres rae. The Euler equaion from he consumer s opimizaion problem implies ha a period he riskfree rae r* is relaed o he one-period marginal subsiuion as follows: 1 1r E s 1. (24) Under he assumpions ha: (i) here is no correlaion beween s and s for all and (ii) +1 8 here is no correlaion beween s and B, (22) can be wrien as: +N +N lim N E [q N B N ] 0. (25) Under hese assumpions, herefore, he appropriae discoun facor is he risk-free ineres rae from he lender s sandpoin insead of he inverse of one plus he real ineres rae on governmen deb. This suggess ha if one is esing he NPG condiion for he Brazilian governmen s exernal deb, say, he appropriae ineres rae is LIBOR, no he acual real ineres rae on Brazilian deb. This is because LIBOR is a reasonable esimae of he lender s risk-free rae. Thus, in evaluaing he NPG in (10), he discoun facor should be he lender s risk-free rae. The real ineres rae faced by he borrower, on he oher hand, is relevan for deermining he ime pah of B +N (via he difference equaion in (3)). Under more general assumpions where here are significan correlaions beween s and s +i and beween s +i and B +i, he ransversaliy condiion in (22) does no direcly imply he a no Ponzi game condiion like (25) holds. When he NPG condiion is no a direc implicaion of he lender s ransversaliy condiion, is i sill an implicaion of opimal behaviour by lenders? The answer is yes. As long as he household uiliy funcion u is sricly increasing and bounded, violaion of he NPG condiion canno be consisen wih opimal household behavior. If he NPG condiion, or equivalenly he PVC, is violaed, i can be shown ha a reallocaion of he household s consumpion over ime in a way ha saisfies he NPG condiion, will raise expeced uiliy: 8 This assumpion implies ha any risk associaed wih B is diversifiable risk, so ha invesors do no demand a risk premium in addiion o he risk-free rae. 18

21 E M j0 j u(c j,m j ). Hence, i can no be opimal for lender s o allow Ponzi game finance. To prove he foregoing claim, firs discoun he period +j household emporal budge consrain back o period. This can be done by muliplying boh sides of he period +j emporal budge consrain by q +j as defined above for j=0,1,...,n. Add he N+1 discouned emporal budge consrains ogeher and ake expecaions of boh sides o obain: E [c q 1 c 1...q N c N ] E [q N B N ] (1r 1 )B 1 E M N j0 q j [f(k j ) - j (1 % j )M j1 M j k j1 k j ]. (26) Now suppose for he sake of argumen ha he presen value consrain in (26) did no hold. Tha is, here exiss some large N such ha E [q+nb +N] > 0. In his case, i is clear ha he household can raise is consumpion c wihou alering is consumpion in he oher periods before +N. Under he assumpion ha he uiliy funcion u is sricly increasing and bounded, a sufficienly large N would make such a reallocaion superior o he allocaion where E [q+nb +N] > 0. Therefore, a violaion of he presen value consrain (26) is no consisen wih he uiliy maximizaion by he lender. Mos of he lieraure esing he NPG condiion has assumed ha he appropriae discoun rae is he real ineres rae on governmen deb (raher han he risk-free rae). In ligh of he above discussion, hese ess are valid even in a sochasic economy. On he oher hand, for a sochasic economy he ransversaliy condiion is differen from he NPG condiion and also a consrain on governmen borrowing. Therefore, i appears ha a valid es of susainabiliy can be based on (23) or (26). 5. An Illusraive Example of Susainable Fiscal Policy This secion lays ou simple examples of susainable and nonsusainable fiscal policies. Consider an economy where GDP (Y) grows exogenously a rae g (independen of 19

22 9 he level of governmen spending and income axaion). The governmen s fiscal policy rule is a very simple one: (1) keep governmen spending G consan as a fracion of GDP, i.e. = G /Y is consan; (2) ax all income wih a fla ax a rae = T/Y, wih no oher sources of revenue; (3) finance any resuling defici resuling from he policies in (1) and (2) by issuing (domesic-currency) bonds a a consan real ineres rae r. Wih his fiscal policy package, he resuling primary surplus equals: SURP (- ) Y. (27) Wih our simple assumpions, SURP grows over ime a rae g, he growh rae of real income. SURP (- )Y 0 (1g). (28) Given he ousanding deb from he previous period, B, he governmen financing -1 consrain in (3) describes he dynamics of deb accumulaion. Ieraing (3) forward and insering (28) for all of he SURP erms o capures he sance of fiscal policy sance yields: B 0 SURP 0 r g (- )Y 0 r g, (29) provided ha he real ineres rae r exceeds he growh rae g (r>g). When g>r, which implies ha he economy is dynamically inefficien, he summaion of discouned fuure surpluses in he PVC is infinie. Is he above fiscal policy package susainable? The calculaion is sraighforward. Find he NPV of he seam of fuure surpluses, defined by he righ-hand-side of (29). If his NPV exceeds (falls shor of) he curren deb, he policy package is susainable (unsusainable) in he sense ha i does no violae he governmen s ineremporal budge 10 consrain. 9 / This is obviously resricive. The recen growh lieraure argues ha fiscal policy can affec he economy s growh rae. See, e.g., he model in Barro (1991). 10 Wheher i is poliically feasible o susain his policy sance is, of course, a differen maer and no he one being esed in he PVC lieraure. 20

23 If he PV of fuure surpluses is negaive, he fiscal policy is unsusainable regardless of he curren deb level. To reierae, if he fiscal sance implies a perpeual primary defici, no amoun of deb reducion can make he fiscal sance susainable. On he oher hand, if he PV of fuure surpluses is posiive bu less han he value of curren deb, a wrie-off of deb equal o he difference: B 0 (- )Y 0 r g would resore fiscal policy susainabiliy. The abiliy o generae a primary surplus is a precondiion for a successful deb reducion program. Noe ha in siuaions where SURP is proporional o GDP and r and g are consan 11 over ime, (29) can be rewrien in erms of he deb/gdp raio. The fiscal sance is susainable if: b 0 surp 0 r g - r g. (30) Here, in conras o he discussion in Secion 2, he choice of denominaor for he raio on he righ-hand-side of (15) can no be chosen arbirarily; i depends wha variable SURP is hypohesized o be proporional o. Furhermore, in deriving (30) from (11) r mus be greaer han g (or he infinie sum in (11) will no converge). The foregoing example is illusraive. For more complicaed ime pahs of governmen spending and axaion and a prespecified iniial deb level, i is sraighforward o implemen fiscal policy susainabiliy analysis using a sandard spreadshee program. See Appendix Economeric Tess of Susainabiliy Several recen sudies on fiscal defici susainabiliy for U.S. fiscal policy are 11 Here s a slighly differen applicaion of he formula. Consider an EMS counry wishing o keep is deb/gdp raio a he Maasrich reay arge of 60%. Wha primary surplus o GDP raio is required for he fiscal sance o be susainable? If he real ineres rae is 5% and he GDP growh rae is 2%, i is easy o show using (30) ha he primary surplus raio mus be 1.8%. 21

24 summarized in Table 1. These sudies are based on differen empirical ess, which in urn depend on he validiy of differen auxiliary assumpions. Hence, hey may yield (and in pracice have yielded) differen conclusions regarding fiscal susainabiliy. This secion describes he various empirical approaches and aemps o explain and reconcile he various findings. The ess are classified ino wo groups. The firs involves ess derived from he NPG condiion using he real ineres rae as he discoun rae. The second group of ess is based on he ransversaliy condiion using marginal rae of subsiuion as discoun facor. =================================================================== Table 1 Recen Sudies of Fiscal Policy Susainabiliy Sudy Counry/ Daa Requiremens Auxiliary Tes Conclusions Sample Assumpions Mehods Flavin- U.S. real primary surplus plus Tes saionary of Boh are Hamilon seigniorage, fiscal defici and saionary, (1986) real sock of deb (a marke deb. implying value) susainable fiscal policy. Wilcox U.S. Marke value of gov deb; Deb follows Tes wheher Weak evidence (1989) ex-pos real reurn on gov general ARIMA discouned deb ha discouned deb. process series is deb is saionary, 22 saionary wih mean zero. ye is mean is nonzero. Hence, fiscal policy is no susainable. Trehan and U.S. real governmen spending, consan real Tes wheher Rejec Walsh (1988) real ineres paymens, ineres rae. fiscal defici nonsaionariy, real revenue, seigniorage inclusive of real implying fiscal G, T may be ineres paymens policy is saionary or is saionary. susainable. nonsaionary Trehan and U.S. Flavin-Hamilon daase Real reurn on Tes for Firs difference of Walsh (1991) gov deb is saionariy of (1) sock of deb is sricly posiive, real defici saionary, bu need no be inclusive of real implying fiscal consan. ineres or (2) policy is firs-difference of susainable. deb.

25 Hakkio-Rush U.S. Real gov revenue and Real ineres rae Tes wheher A coinegraion (1991) 1950:II- spending inclusive of real is saionary. gov revenue and relaionship is 1988:IV ineres. Gov spending spending found for he and revenue are inclusive of enire sample, bu difference- ineres are no for he subsaionary. coinegraed. period 1976:III- 1988:IV. Hence, recen fiscal policy is no susainable. Corsei- OECD Ne general gov deb; ex Tes saionariy Resuls are mixed Roubini pos reurn on deb. of discouned for OECD (1991) deb and he counries sudied. exisence of posiive drif or ime rend. Ahmed- U.S Real gov ax revenue, s +j G +j and Tes wheher real For boh he U.S. Rogers 1992 expendiure, and real s +j T +j are gov ax revenue, and he U.K., a (1995) ineres paymens difference expendiure, and coinegraion U.K. saionary where real ineres relaionship wih s +j is he lender s paymens are vecor marginal rae of coinegraed wih (-1,1,1) is found, subsiuion. vecor implying ha (-1,1,1). U.S. fiscal policy is susainable. Tesing NPG condiion The lieraure esing he NPG condiion originaed wih he pioneering work of Hamilon and Flavin (1984). They esed a version of he NPG condiion where he ex pos real ineres rae on governmen deb in each period r was replaced by he average real ineres rae denoed by r. This involves rewriing he governmen budge consrain (3) as: B (1r)B 1 SURP (r r)b 1 (1r)B 1 SURP v, (31) where he error erm v capures he deviaion of he ineres rae from is average value. Ieraing forward yields: 23

26 B 1 lim N B N (1r) (N1) M j0 (1r) (j1) SURP j n, (32) where n M j0 (1r) (j1) v j is assumed o be mean zero saionary. Taking expecaions on boh sides of (32) yields: B 1 E lim N (1r) (N1) B N E M j0 (1r) (j1) SURP j. (33) 12 Hamilon and Flavin es wheher E lim N (1r) (N) B N 0. (34) or, equivalenly: B 1 E M j0 (1r) (j1) SURP j. (35) For siuaions where he expeced rae of reurn on governmen deb is consan (i.e., E r = r, +i 13 for i=1,2,...) and r is uncorrelaed wih SURP s and B s for all and s, he PVC in (20) becomes (35) Equaions (34) or (35) are also used in susainabiliy ess by Trehan and Walsh (1988,1991), Hakkio and Rush (1991), and Tanner and Liu (1994). 13 The assumpion of no correlaion beween real ineres raes and deficis or deb is a very srong one. Presumably, increases in governmen spending ha lead o higher borrowing will cause an increase in real ineres raes (excep in he case of a small open economy wih perfec capial mobiliy). 14 Here he PVC is expressed as he same form as he ransversaliy condiion derived in Appendix 1. Asympoically i is no differen han he expression in (34). Because of he 24

27 Hamilon and Flavin (1984) consider he class of deb processes saisfying E lim N B N (1r) N A 0, (36) where A can be any consan. For his class of deb processes, he governmen budge 0 consrain in (32) can be rewrien as B 1 A 0 (1r) M j0 (1r) (j1) SURP j n. (37) Among his class of deb processes, only hose wih A = 0 saisfy he PVC. Tesing he PVC 0 15 amouns o esing wheher A 0 is zero or no. From (37), i can be seen ha if -(j+1) (1+r) SURP is saionary, A is equal o zero if and only if B is also saionary. j=0 +j 0-1 Therefore, if boh SURP and B are saionary ime series processes, he PVC in (35) will necessarily be saisfied. Employing augmened Dicky Fuller (ADF) ess for he presence of uni roos, Hamilon and Flavin (1984) rejec he null hypoheses ha SURP and B are nonsaionary. Therefore, hey conclude ha he PVC holds, implying ha U.S. fiscal policy is susainable. Kremers (1988), however, argues convincingly Hamilon and Flavin s ADF regressions were misspecified by no including sufficien lagged differences of he dependen variable o eliminae serially correlaion in he residuals. He claims ha he addiion of a second lagged dependen variable produces a correcly specified regression. Wih his specificaion, he ADF es indicaes ha he deb series B is nonsaionary due o he presence of a uni roo. algebraic manipulaion in (31), however, he value of B in he wo expressions will differ somewha a finie horizons. 15 Noe ha hese ess have he same form as hose esing for he presence of (deerminisic) speculaive bubbles in financial asse pricing lieraure. 25

28 He herefore concludes ha he PVC does no hold, overurning Hamilon and Flavin s conclusion ha U.S. fiscal policy is susainable. The Hamilon and Flavin mehod is limied in a couple of respecs. Firs, i assumes he deb process is in he class saisfying (36). Hence i is imporan o deermine wheher his assumpion is oo resricive. Second, he Hamilon-Flavin es does no handle siuaions where SURP is nonsaionary, ye his is no necessary for fiscal susainabiliy. Finally, i is desirable o allow for sochasic expecaions of he real rae of reurn in he susainabiliy ess. Trehan and Walsh (1991) exend he Hamilon and Flavin mehod in hese wo respecs. Firs, hey prove ha he Hamilon and Flavin mehod is valid as long as he deb series can be characerized as a general auoregressive moving average (ARIMA) process. I does no have o saisfy (36) wih A consan. Trehan and Walsh demonsrae ha if SURP 0 is saionary, he simplified PVC (35) holds if and only if B is also saionary. Trehan and Walsh also consruc susainabiliy ess for siuaions where SURP happens o be a nonsaionary ime series process. They do his by using he resricion ha (35) imposes on he ime series properies of B and SURP. The paricular proposiion -1 derived in Trehan and Walsh (1991, proposiion 1, p.209) is: If he evoluion of B is given by (3) wih E(r +i I +i ) = r for all i 1 [a consan expeced ineres rae] and (1-L)SURP is a mean zero saionary wih [i.e. for some in he range] 0 < (1+r), hen [he NPG condiion] holds if and only if here exiss a linear combinaion of SURP and B -1 ha is saionary. The procedure for esing for he presence of his linear combinaion is as follows. Firs, deermine he value or range of values of ha make (1-L)SURP a mean-zero saionary series. If SURP iself is saionary, hen (1-L)SURP mus also be saionary for all in he range [0,1]. In his case, (35) holds if and only if B is also saionary. This is -1 26

29 precisely he Hamilon-Flavin es. In he siuaion where SURP is difference saionary (i.e., = 1), he PVC in (35) holds if and only if he convenional defici, rb - SURP, is -1 saionary. This implies ha B and SURP are coinegraed wih coinegraion -1 vecor (r, -1). Finally, for he case where he larges roo in he SURP process exceeds uniy bu is less han 1+r (1< < (1+r)), (35) holds if and only if SURP and B are -1 coinegraed. In his case, he coinegraing vecor need no be (r,-1). The laer is called he Trehan-Walsh coinegraion es below. Trehan and Walsh (1991) applied heir coinegraion es o U.S. deb and primary deficis over he period , he same period employed in Hamilon and Flavin (1984). Their saisical ess indicae ha SURP is saionary (i.e., 0 < 1), bu B is no. Therefore hey conclude ha he governmen budge process is no susainable. This resul is consisen wih he conclusion in Kremer s (1988) reconsideraion of he Hamilon-Flavin analysis. The governmen emporal budge consrain (3) depends only on SURP, no is decomposiion ino, say, non-ineres governmen spending G and ax revenue T. By decomposing SURP in his way, however, i is possible o deermine he resricion ha he PVC imposes on he ime series properies of governmen spending and revenue. Hakkio and Rush (1991) propose esing he PVC in (34) by checking wheher he governmen expendiure inclusive of ineres paymen G + r B is coinegraed wih T and wheher he -1 coinegraion vecor is (1,-1). The validiy of heir es depends on several auxiliary assumpions: (i) r is saionary wih uncondiional mean r and (ii) boh G + (r -r)b and T -1 follow uni roo processes (i.e. he = 1 case above). Hakkio and Rush apply heir es o U.S. daa for he period 1950:II o 1988:IV as well as he sub-samples: 1964:I-1988:IV and 1976:III-1988:IV. For he laer wo periods, 27

30 hey conclude here is no coinegraion beween T and G + r B. Like Trehan and Walsh -1 and Kremers, herefore, hey reach he conclusion ha recen US fiscal policy is no susainable once he evidence from he 1980s is included in he daase. The similariy in he Trehan-Walsh and Hakkio-Rush findings is no coincidence. If he auxiliary assumpions wo approaches are saisfied, he wo ess are equivalen. Tha is, if G + r B is coinegraed -1 wih T and he coinegraion vecor is (1,-1), hen 1(G r B 1 ) 1T r B 1 SURP (r r)b 1 rb 1 SURP (38) mus be saionary. The coinegraion of G + r B and T wih a coinegraion vecor (1,-1) -1 means ha he lef-hand side of (38) is saionary. Under he assumpion ha r is saionary wih uncondiional mean r, r - r and hence (r -r)b are saionary. Therefore, G + r B - T -1-1 is saionary if and only if rb - SURP is saionary. -1 Wha if he assumpion of a consan expeced real raes of reurn on governmen deb 16 is no provide a good characerizaion of he daa? The Hakkio-Rush and Trehan-Walsh coinegraion ess, as well as he Hamilon-Flavin es, are no longer valid. Wilcox (1989) presens a saionariy es ha does no require expeced real ineres raes o be consan. In he presence of sochasic expeced real raes, one can use he ex pos real raes o discoun he governmen deb ousanding in period o a fixed poin, say, period 0. Then he ime series characerisics of he discouned deb series q+ib +i can be examined. If his series is saionary wih mean zero, hen he NPG condiion (25) mus hold. Applying 16 Using daa for eigheen OECD counries, Rose s (1988) economeric examinaion of nominal ineres raes and inflaion raes implies ha real ineres rae are, in fac, nonsaionary. Even if he real rae was saionary, he assumpion of a consan expeced rae implies he absence of serial correlaion in he series, which is clearly conradics he facs for U.S. T-bill raes. 28

31 his es o US fiscal policy for he period , Wilcox finds ha he discouned deb series is no (mean) saionary. We can no be sure from his evidence ha recen US fiscal policy is no susainable, however, since mean-zero saionary of q+ib +i is only a sufficien, no a necessary, condiion for he PVC o hold. Suppose, for example, ha q+ib +i is exponenially decaying oward zero, he PVC clearly holds even hough he discouned deb series is nonsaionary. Trehan and Walsh (1991, proposiion 2) also presen a es ha allows for imevarying expeced real raes. They show ha, if r is a sochasic process sricly bounded below by >0, a sufficien condiion for he presen value consrain o hold is ha (1-L)B is saionary. The reasoning behind his resul is sraighforward. If B is difference saionary, i can conain a ime rend of order no greaer han one. Thus, B grows a mos linearly wih he ime. If real raes are sricly posiive, he discoun facor q will decay exponenially. Therefore he presen value of B, q B, mus go o zero as goes o infiniy. Applying his es o US fiscal policy for he period 1960 o 1984, Trehan and Walsh 17 found he firs difference of deb o be saionary. As his is a sufficien condiion for he PVC o hold, hey conclude ha he recen US fiscal policy is susainable. Noe ha his conclusion conradics he resuls of heir coinegraion es discussed above. Trehan and Walsh inerpre his finding o imply ha he defici process is consisen wih susainabiliy, bu ha he assumpion of a consan expeced real rae is a bad approximaion o he daa. 17 Noe ha boh he Wilcox es and he Trehan-Walsh saionariy es revolve around sufficien condiions for he deb process o saisfy he presen value consrain. If hese sufficien condiions are violaed, herefore, he wo ess are inconclusive regarding fiscal policy susainabiliy. 29